Question

The subsoil at a site consists of a fine sand layer lying in between a clay layer at top and a silt layer at bottom. the co-efficient of permeability of the sand is 100 times that of clay and 20 times that of silt, while the thickness of each layer is the same and is equal to h. find out the ratio of the equivalent co-efficient of permeability of the deposit in directions parallel and perpendicular to the bedding planes.

Answer 1

The problem of land degradation

PRESSURES ON THE REGION'S AGRICULTURAL LAND ARE LEADING TO EXTENSIVE LAND DEGRADATION. THE CAUSES ARE POVERTY, LAND SHORTAGE AND INCREASING POPULATIONS

In 1992 developing countries in Asia and the Pacific accounted for just less than 54 percent of the world population - nearly 3000 million people. Yet these countries had only 17 percent of the world's land resources.

Even so, countries in Asia and the Pacific are relatively well fed compared, for example, to much of Africa and parts of Central and South America. This is because they have made profitable use of new agricultural technology, such as fertilizers, high-yielding crop varieties, mechanization and irrigation. During the period ]961-85, 93 percent of the region's increase in cereal production was due to increased production inputs. As a result food production has more than kept pace with population increase.

While agricultural productivity has risen dramatically, the cost in land degradation has been high. Large areas of the region's cropland, grassland, woodland and forest are now seriously degraded. Water and wind erosion are the major problems but salinity, sodicity and alkalinity are also widespread; water tables have been over-exploited; soil fertility has been reduced; and where mangrove forest has been cleared for aquaculture or urban expansion, coastal erosion has been a common result. Finally, urban expansion has become a major form of land degradation, removing large areas of the best agricultural land from production.

The effect of these forms of land degradation on cereal production has so far been masked by the increasing levels of agricultural inputs that are used. However, production of other crops, such as pulses, roots and tubers, has now begun to decline. It is no coincidence that these crops arc grown on land with low production potential, where rates of land 

Answer 2

Given details:

Co-efficient of permeability of sand is 100 times that of clay, and 20 times that of silt layer of soil.

Thickness of each layer is equal and is denoted by 'h'.

Solution:

Let the co-efficient of permeability of clay layer be 'k'

So, co-efficient of permeability of  sand layer = 100k

And, co-efficient of permeability of silt layer= 100k / 20 = 5k

We know that, formula for equivalent co-efficient of permeability of the deposit in directions parallel to the bedding planes is given by:

keq(horizontal) = (k1 * H1 + k2 * H2+ k3* H3) / (H1 + H2 + H3)

Here, keq (horizontal)= (k * h + 100k * h + 5k * h) / (h+h+h)

= h* k* 106 / 3*h

keq (horizontal) = 35.333 k

We know that, formula for equivalent co-efficient of permeability of the deposit in directions perpendicular to the bedding planes is given by:

keq (vertical) =  (H1 + H2 + H3) / ( H1/k1 + H2/k2 +H3/k3)

= (h+h+h)  /  ( h/k + h/100k + h/5k )

= 3 * h / [ (h/k) * ( 500+ 5 + 100) / 500) ]

= 3k / 1.21

keq (vertical) =  2.479 k

Answer:

Ratio = 35.333k / 2.479k = 14.25